Solve by substitution method
7m+n=27
m-8n=69
What is the solution of the system?
I've showed you how to do these several times. Your turn.
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To solve the system of equations using the substitution method, we need to first solve one equation for one variable and then substitute that expression into the other equation. Let's solve the second equation for m.
The second equation is:
m - 8n = 69
Step 1: Isolate m.
Add 8n to both sides of the equation:
m = 69 + 8n
Now we have an expression for m in terms of n. We can substitute this expression into the first equation.
The first equation is:
7m + n = 27
Step 2: Substitute the expression for m into the first equation.
Replace m with 69 + 8n in the first equation:
7(69 + 8n) + n = 27
Now we have an equation with only one variable, n. We can solve for n.
Step 3: Solve for n.
Multiply 7 by 69 and 7 by 8n:
483 + 56n + n = 27
Combine like terms:
57n + 483 = 27
Subtract 483 from both sides of the equation:
57n = 27 - 483
57n = -456
Divide both sides of the equation by 57:
n = -456/57
n = -8
Now that we have the value of n, we substitute it back into the expression for m to find its value.
Step 4: Substitute n = -8 into the expression for m.
m = 69 + 8n
m = 69 + 8(-8)
m = 69 - 64
m = 5
So the solution to the system of equations is m = 5 and n = -8.